Abundant Symmetries and Exact Compacton—Like Structures in the Two—Parameter Family of the Estevez—Mansfield—Clarkson Equations

作     者：YANZhen－Ya 

作者机构：DepartmentofAppliedMathematicsDalianUniversityofTechnologyDalian116024China 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2002年第37卷第1期

页      面：27-34页

核心收录：

学科分类：0809[工学-电子科学与技术（可授工学、理学学位）] 07[理学] 070205[理学-凝聚态物理] 08[工学] 070104[理学-应用数学] 0701[理学-数学] 0702[理学-物理学] 

基　　金：国家重点基础研究发展计划(973计划) 国家博士基金 国家自然科学基金 

主　　题：非线性方程 非线性色散 类孤子波解 

摘      要：The two-parameter family of Estevez-Mansfield-Clarkson equations with fully nonlinear dispersion (called E(m, n) equations), (uzm)zzr + γ(unzur)z + urr = 0 which is a generalized model of the integrable Estevez-MansfieldClarkson equation u + γ(uzuzr +uzzur) +urr = 0, is presented. Five types of symmetries of the E(m, n) equation are obtained by making use of the direct reduction method. Using these obtained reductions and some simple tranaformations,we obtain the solitary-like wave solutions of E(1, n) equation. In addition, we also find the compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions, they reemerge with the same coherent shape) orE(3, 2) equation and E(m, m- 1) for its potentials, say, uz, and compacton-like solutions of E(m, m- 1)equations, respectively. Whether there exist compacton-like solutions of the other E(m, n) equation with m ≠ n + 1 is still an open problem.